Integral photography and lenticular three-dimensional image schemes (see Takanori Okoshi, “Three-Dimensional Imaging Techniques”, Academic Press, 1976) are known as methods of forming a stereoscopic image. However, such methods of forming a stereoscopic image rely upon photographic methods. For example, a lenticular three-dimensional image is obtained by acquiring images that are the result of photographing a subject from a number of viewpoints and printing these images on a single photographic plate via a lenticular sheet, which has extremely small semicircular cylindrical convex lenses (cylindrical lens elements) disposed in parallel on one side thereof. However, this method involves problems A to C below.
A. Since images from a number of viewpoints of the subject are necessary, elaborate photographic equipment such as a multiocular camera is required.
B. Likewise, elaborate printing equipment is necessary for forming the stereoscopic image.
C. Photography and printing require adjustments and experience even if the above equipment is used.
In view of the aforementioned problems, various proposals utilizing digital photographic techniques have been made in recent years to achieve the formation of stereoscopic images through a simple arrangement.
For example, the present applicant has proposed a system in which  stereoscopic photography is simplified by mounting a stereoscopic photograph adapter on a digital camera, generating a multiple viewpoint image sequence from a captured stereo image and printing a three-dimensional image, and observing this image through a lenticular sheet, thereby simplifying the formation of the stereoscopic image. Further, the structure of the optical member, thereby converting the multivalued image to a binary dot pattern.
The present applicant has further proposed a technique in which a video signal exhibiting multiple parallax is converted to a binary video signal by an error diffusion processing circuit, whereby it becomes possible to output the image to a binary printer, as illustrated in the specification of Japanese Patent Application Laid-Open No. 9-102968. However, a three-dimensional image generated from a multiple viewpoint image sequence requires much more image data than an ordinary image. If a binary image conversion based upon the error diffusion method is applied to such a multivalued image, processing time is prolonged.
The present applicant has further proposed a technique in which when a multivalued image is converted to a binary image, the error diffusion method and a density pattern method are used conjointly to achieve both the high tonal representation of the error diffusion method and the high processing speed of the density pattern method, as illustrated in the specification of Japanese Patent Application Laid-Open No. 7-38766. The present applicant has further proposed a technique in which a plurality of density patterns are prepared and used by being switched among selectively, thereby making it possible to obtain a greater improvement in image quality, as illustrated in the specification of Japanese Patent Application Laid-Open No. 8-142411. If these techniques are applied to the binarization of a three-dimensional image, both high image quality and high processing speed can be achieved.
However, if the above-described error diffusion method or density pattern method is simply applied to processing for binarizing a three-dimensional image in the prior art, a problem arises.
Specifically, fringes corresponding to a difference frequency |n·fP−m·fL| (where n,m are positive integers) that is a whole-number multiple of the difference between spatial frequencies are produced in the direction in which the cylindrical lens elements are arranged, where fL represents the spatial frequency corresponding to the pitch at which the cylindrical lens elements of the lenticular sheet repeat, and fP represents the spatial frequency corresponding to the direction in which the cylindrical lens elements of the lenticular sheet repeat (this direction shall be referred to as the “cylindrical-lens array direction” below).
The smaller n, m are, the greater the contrast of the fringes. Since fP>fL holds, it is preferred that fP be as closed to fL as possible. That is, the contrast of the fringes increases and the fringes become more noticeable if the spatial frequency corresponding to the cylindrical-lens array direction in the black-and-white density pattern of the printer is low. In order to reduce the occurrence of fringes, therefore, it is required that the black-and-white density pattern of the printer be controlled taking into account the cylindrical-lens array direction.